{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ODE solver\n",
    "\n",
    "In this notebook, we show some examples of solving an ODE model. For the purposes of this example, we use the Scipy solver, but the syntax remains the same for other solvers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[33mWARNING: You are using pip version 22.0.4; however, version 22.3.1 is available.\n",
      "You should consider upgrading via the '/home/mrobins/git/PyBaMM/env/bin/python -m pip install --upgrade pip' command.\u001b[0m\u001b[33m\n",
      "\u001b[0mNote: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install \"pybamm[plot,cite]\" -q    # install PyBaMM if it is not installed\n",
    "import os\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import pybamm\n",
    "\n",
    "os.chdir(pybamm.__path__[0] + \"/..\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integrating ODEs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In PyBaMM, a model is solved by calling a solver with `solve`. This sets up the model to be solved, and then calls the method `_integrate`, which is specific to each solver. We begin by setting up and discretising a model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create model\n",
    "model = pybamm.BaseModel()\n",
    "u = pybamm.Variable(\"u\")\n",
    "v = pybamm.Variable(\"v\")\n",
    "model.rhs = {u: -v, v: u}\n",
    "model.initial_conditions = {u: 2, v: 1}\n",
    "model.variables = {\"u\": u, \"v\": v}\n",
    "\n",
    "\n",
    "# Discretise using default discretisation\n",
    "disc = pybamm.Discretisation()\n",
    "disc.process_model(model);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the model can be solved by calling `solver.solve` with a specific time vector at which to evaluate the solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1300x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solve ########################\n",
    "t_eval = np.linspace(0, 5, 30)\n",
    "ode_solver = pybamm.ScipySolver()\n",
    "solution = ode_solver.solve(model, t_eval)\n",
    "################################\n",
    "\n",
    "# Extract u and v\n",
    "t_sol = solution.t\n",
    "u = solution[\"u\"]\n",
    "v = solution[\"v\"]\n",
    "\n",
    "# Plot\n",
    "t_fine = np.linspace(0, t_eval[-1], 1000)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(13, 4))\n",
    "ax1.plot(t_fine, 2 * np.cos(t_fine) - np.sin(t_fine), t_sol, u(t_sol), \"o\")\n",
    "ax1.set_xlabel(\"t\")\n",
    "ax1.legend([\"2*cos(t) - sin(t)\", \"u\"], loc=\"best\")\n",
    "\n",
    "ax2.plot(t_fine, 2 * np.sin(t_fine) + np.cos(t_fine), t_sol, v(t_sol), \"o\")\n",
    "ax2.set_xlabel(\"t\")\n",
    "ax2.legend([\"2*sin(t) + cos(t)\", \"v\"], loc=\"best\")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that, where possible, the solver makes use of the mass matrix and jacobian for the model. However, the discretisation or solver will have created the mass matrix and jacobian algorithmically, using the expression tree, so we do not need to calculate and input these manually."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The solution terminates at the final simulation time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'final time'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution.termination"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Events\n",
    "\n",
    "It is possible to specify events at which a solution should terminate. This is done by adding events to the `model.events` dictionary. In the following example, we solve the same model as before but add a termination event when `v=-2`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1300x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create model\n",
    "model = pybamm.BaseModel()\n",
    "u = pybamm.Variable(\"u\")\n",
    "v = pybamm.Variable(\"v\")\n",
    "model.rhs = {u: -v, v: u}\n",
    "model.initial_conditions = {u: 2, v: 1}\n",
    "model.events.append(pybamm.Event(\"v=-2\", v + 2))  # New termination event\n",
    "model.variables = {\"u\": u, \"v\": v}\n",
    "\n",
    "# Discretise using default discretisation\n",
    "disc = pybamm.Discretisation()\n",
    "disc.process_model(model)\n",
    "\n",
    "# Solve ########################\n",
    "t_eval = np.linspace(0, 5, 30)\n",
    "ode_solver = pybamm.ScipySolver()\n",
    "solution = ode_solver.solve(model, t_eval)\n",
    "################################\n",
    "\n",
    "# Extract u and v\n",
    "t_sol = solution.t\n",
    "u = solution[\"u\"]\n",
    "v = solution[\"v\"]\n",
    "\n",
    "# Plot\n",
    "t_fine = np.linspace(0, t_eval[-1], 1000)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(13, 4))\n",
    "ax1.plot(t_fine, 2 * np.cos(t_fine) - np.sin(t_fine), t_sol, u(t_sol), \"o\")\n",
    "ax1.set_xlabel(\"t\")\n",
    "ax1.legend([\"2*cos(t) - sin(t)\", \"u\"], loc=\"best\")\n",
    "\n",
    "ax2.plot(\n",
    "    t_fine,\n",
    "    2 * np.sin(t_fine) + np.cos(t_fine),\n",
    "    t_sol,\n",
    "    v(t_sol),\n",
    "    \"o\",\n",
    "    t_fine,\n",
    "    -2 * np.ones_like(t_fine),\n",
    "    \"k\",\n",
    ")\n",
    "ax2.set_xlabel(\"t\")\n",
    "ax2.legend([\"2*sin(t) + cos(t)\", \"v\", \"v = -2\"], loc=\"best\")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the solution terminates because the event has been reached"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'event: v=-2'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution.termination"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "event time:  [3.78510677] \n",
      "event state [-0.99995359 -2.        ]\n"
     ]
    }
   ],
   "source": [
    "print(\"event time: \", solution.t_event, \"\\nevent state\", solution.y_event.flatten())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "The relevant papers for this notebook are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] Joel A. E. Andersson, Joris Gillis, Greg Horn, James B. Rawlings, and Moritz Diehl. CasADi – A software framework for nonlinear optimization and optimal control. Mathematical Programming Computation, 11(1):1–36, 2019. doi:10.1007/s12532-018-0139-4.\n",
      "[2] Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, and others. Array programming with NumPy. Nature, 585(7825):357–362, 2020. doi:10.1038/s41586-020-2649-2.\n",
      "[3] Valentin Sulzer, Scott G. Marquis, Robert Timms, Martin Robinson, and S. Jon Chapman. Python Battery Mathematical Modelling (PyBaMM). Journal of Open Research Software, 9(1):14, 2021. doi:10.5334/jors.309.\n",
      "[4] Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, and others. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nature Methods, 17(3):261–272, 2020. doi:10.1038/s41592-019-0686-2.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "pybamm.print_citations()"
   ]
  }
 ],
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